Fuzzy Logic and Neural Networks: Basic Concepts and Applications

Cover......Page 1
Preface......Page 8
Contents......Page 10
1.1 Fuzzy Logic (FL)......Page 20
1.2 Neural Networks (NN)......Page 21
Question Bank......Page 23
References......Page 24
2.2 What is Fuzzy Logic?......Page 25
2.3 Historical Background......Page 27
2.6.1 Fuzzy Set......Page 28
2.6.5 Convex Fuzzy Set......Page 30
2.6.7 Quasi Fuzzy Number......Page 31
2.6.8 Triangular Fuzzy Number......Page 32
2.6.10 Subsethood......Page 33
2.6.14 Fuzzy Point......Page 34
2.7.2 Union......Page 35
Question Bank......Page 36
References......Page 37
3.2.1 Classical N-Array Relation
......Page 38
3.2.9 Total Order......Page 39
3.3.1 Intersection......Page 40
3.3.2 Union......Page 41
3.3.3 Projection......Page 42
3.3.5 Shadow of Fuzzy Relation......Page 43
3.3.6 Sup-Min Composition of Fuzzy Relations......Page 45
References......Page 46
4.1 Introduction......Page 48
4.2 Fuzzy Implications......Page 49
4.3 Modifiers
......Page 52
4.3.1 Linguistic Variables......Page 53
4.3.2 the Linguistic Variable Truth......Page 54
Question Bank......Page 57
References......Page 58
5.1 Introduction......Page 60
5.2.3 Disjunction Rule......Page 62
5.2.6 Compositional Rule of Inference......Page 63
5.3.1 Basic Property......Page 64
5.3.3 Subset......Page 65
5.3.4 Superset......Page 66
Question Bank......Page 69
References......Page 70
6.2 Triangular Norm
......Page 73
6.3 Triangular Conorm
......Page 74
6.5 t-Conorm-Based Union......Page 76
6.6.1 An Averaging Operator is a Function......Page 77
6.6.2 Ordered Weighted Averaging......Page 79
6.7 Measure of Dispersion or Entropy of an Owa Vector......Page 82
6.9 Larsen System......Page 85
6.10 Defuzzification......Page 86
References......Page 87
7.2 Fuzzy Rule-Base System......Page 90
7.3 Inference Mechanisms in Fuzzy Rule-Base Systems......Page 91
7.3.2 Tsukamoto Inference Mechanism......Page 92
7.3.3 Sugeno Inference Mechanism......Page 94
7.3.5 Simplified Fuzzy Reasoning......Page 96
References......Page 98
8.2 Basic Feedback Control System......Page 100
8.3.2 Mamdani Type of Fuzzy Logic Control......Page 101
8.3.3 Fuzzy Logic Control Systems......Page 103
8.4 Defuzzification Methods......Page 105
8.4.3 Middle-of-Maxima......Page 106
8.4.5 Height Defuzzification......Page 107
8.5 Effective of Fuzzy Logic Control Systems......Page 108
References......Page 110
9.1 Why Use Fuzzy Logic?......Page 113
9.2 Applications of Fuzzy Logic......Page 114
9.4.1 Traffic Accidents and Traffic Safety......Page 115
9.4.3 Application......Page 116
9.4.4 Membership Functions......Page 117
9.4.7 Conclusions......Page 118
9.5.1 The Mechanics of Fuzzy Logic......Page 119
9.5.2 Fuzzification......Page 120
9.5.3 Rule Application......Page 121
9.5.4 Defuzzification......Page 122
9.6 Fuzzy Logic Model for Grading of Apples......Page 123
9.6.2 Materials and Methods......Page 124
9.6.3 Application of Fuzzy Logic
......Page 125
9.6.4 Fuzzy Rules......Page 127
9.6.5 Determination of Membership Functions......Page 128
9.6.6 Defuzzification......Page 129
9.6.7 Results and Discussion......Page 130
9.7.1 The Non-Fuzzy Approach......Page 131
9.7.2 The Fuzzy Approach......Page 135
9.7.3 Some Observations......Page 136
References......Page 137
10.2 Biological Neural Network
......Page 140
10.3 A Framework for Distributed Representation......Page 141
10.3.2 Connections Between Units......Page 142
10.3.3 Activation and Output Rules......Page 143
10.5.1 Paradigms of Learning......Page 144
10.6.1 Notation......Page 145
10.6.2 Terminology......Page 146
References......Page 147
11.2 Networks with Threshold Activation Functions......Page 148
11.3.2 Convergence Theorem......Page 150
11.4 Adaptive Linear element (Adaline)......Page 152
11.5 The Delta Rule......Page 153
11.6 Exclusive-or Problem
......Page 154
11.7 Multi-Layer Perceptrons can do Everything
......Page 156
References......Page 157
12.2 Multi-Layer Feed-Forward Networks......Page 158
12.3 The Generalised Delta Rule......Page 159
12.3.1 Understanding Back-Propagation......Page 161
12.4.1 Weight Adjustment with Sigmoid Activation Function......Page 162
12.4.3 Learning Per Pattern......Page 163
12.6 Deficiencies of Back- Propagation......Page 165
12.7 Advanced Algorithms......Page 167
12.8 How Good are Multi-Layer Feed-Forward Networks?
......Page 170
12.8.1 The Effect of the Number of Learning Samples......Page 171
12.9 Applications......Page 172
References......Page 174
13.2 The Generalized Delta-Rule in Recurrent Networks......Page 176
13.2.1 The Jordan Network......Page 177
13.2.2 The Elman Network......Page 178
13.3 The Hopfield Network
......Page 180
13.3.1 Description......Page 181
13.3.2 Hopfield Network as Associative Memory......Page 182
13.3.4 Hopfield Networks for Optimization Problems......Page 183
13.4 Boltzmann Machines......Page 184
References......Page 186
14.1 Introduction......Page 188
14.2.1 Clustering......Page 189
14.2.3 Counter Propagation......Page 193
14.2.4 Learning Vector Quantisation......Page 195
14.3 Kohonen Network......Page 196
14.4 Principal Component Networks
......Page 198
14.4.1 Normalized Hebbian Rule......Page 199
14.4.3 More Eigenvectors......Page 200
14.5.1 Background: Adaptive Resonance Theory......Page 201
14.5.2 ART 1: The Simplified Neural Network Model......Page 202
14.5.3 Operation......Page 203
14.5.4 ART 1: The Original Model......Page 204
14.5.5 Normalization of the Original Model......Page 205
14.5.6 Contrast Enhancement......Page 206
References......Page 207
15.2 The Critic......Page 209
15.3 The Controller Network......Page 210
15.4 Barto's Approach: The ASE-ACE Combination......Page 211
15.4.1 Associative Search......Page 212
15.4.3 The Cart-Pole System......Page 213
15.5 Reinforcement Learning Versus Optimal Control......Page 214
References......Page 216
16.1 Introduction......Page 218
16.2.2 Inverse Kinematics......Page 219
16.2.5 End-Effector Positioning......Page 220
16.2.6 Camera-Robot Coordination in Function Approximation......Page 221
16.2.6a Approach-1: Feed-Forward Networks
......Page 222
16.2.6b Approach 2: Topology Conserving Maps......Page 225
16.2.7 Robot Arm Dynamics......Page 226
16.3 Detection of Tool Breakage in Milling Operations......Page 229
16.3.1 Unsupervised Adaptive Resonance Theory (ART) Neural Networks......Page 230
16.3.2 Results and Discussion
......Page 232
References......Page 234
17.2.1 Sequential Hybrid Systems......Page 236
17.2.3 Embedded Hybrid Systems......Page 237
17.3 Fuzzy Logic in Learning Algorithms......Page 238
17.4 Fuzzy Neurons......Page 239
17.5 Neural Networks as Pre-Processors or Post-Processors......Page 240
17.6 Neural Networks as Tuners of Fuzzy Logic Systems......Page 241
17.8 Commitee of Networks......Page 242
17.9 FNN Architecture Based on Back Propagation......Page 243
17.9.1 Strong L-R Representation of Fuzzy Numbers......Page 245
17.9.2 Simulation......Page 247
17.10 Adaptive Neuro-Fuzzy Inference System (ANFIS)......Page 248
17.101 ANFIS Structure......Page 250
References......Page 251
18.2 Tool Breakage Monitoring System for End Milling......Page 252
18.2.1 Methodology: Force Signals in the End Milling Cutting Process......Page 253
18.2.2 Neural Networks......Page 254
18.2.3 Experimental Design and System Development Experimental Design......Page 256
18.2.4 Neural Network-BP System Development......Page 257
18.2.5 Finding and Conclusions......Page 260
18.3.1 Adaptive Neuro-Fuzzy Inference System......Page 262
18.3.2 Learning Method of ANFIS......Page 264
18.3.3 Model of Combustion......Page 265
18.3.4 Optimization of the PI-Controllers Using Genetic Algorithms......Page 266
References......Page 270
Index......Page 272